In this paper, we consider fully nonlinear parabolic problems involving the fractional Laplacian. Hopf type lemmas for both on bounded domain \(\varOmega \) with smooth boundary and half space are obtained. When \(\varOmega \) is a ball or the whole space, we obtain the radial symmetry results of positive solutions. Our results are an extension of Li-Nirenberg [19], Li-Chen [18] and Wang-Chen [24].

中文翻译：

---

涉及分数拉普拉斯算子的完全非线性抛物方程的径向对称性和 Hopf 引理

在本文中，我们考虑涉及分数拉普拉斯算子的完全非线性抛物线问题。获得了具有平滑边界和半空间的有界域\(\varOmega \)上的 Hopf 类型引理。当\(\varOmega \)是一个球或整个空间时，我们得到正解的径向对称结果。我们的结果是对 Li-Nirenberg [19]、Li-Chen [18] 和 Wang-Chen [24] 的扩展。